The Peliti construction [1]}, [2]}
likewise replaces \(a^{\dagger }\)  and \(a\)  in \(\mathcal {L}\)  with the
coherent-state parameters that are their eigenvalues. Stationary
trajectories arise in the saddle-point approximation of the functional
integral (REF ), where they are solutions to the
vanishing of the variational derivative of \(S\) . These stationary paths
are those which provide the eikonal approximation to the probability
densityFor a discussion of when this property does or does
not apply to stationary paths used to calculate generating functions
and functionals, see [3]}. It will always apply to
the solutions computed here. For much earlier work on a condition
equivalent to \(\mathcal {L} = 0\)  as a property of stationary
distributions, see [4]}. and \(\mathcal {L}\! \left( {\xi }^{\dagger } , \xi \right) = 0\)  is a property of these
paths.
